ON THE CHARACTERISATION OF ALTERNATING GROUPS BY CODEGREES

IF 0.6 4区数学 Q3 MATHEMATICS

Bulletin of the Australian Mathematical Society Pub Date : 2024-01-26 DOI:10.1017/s0004972723001429

MALLORY DOLORFINO, LUKE MARTIN, ZACHARY SLONIM, YUXUAN SUN, YONG YANG

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引用次数: 0

Abstract

Let G be a finite group and

$\mathrm {Irr}(G)$

the set of all irreducible complex characters of G. Define the codegree of

$\chi \in \mathrm {Irr}(G)$

$\mathrm {cod}(\chi ):={|G:\mathrm {ker}(\chi ) |}/{\chi (1)}$

and let

$\mathrm {cod}(G):=\{\mathrm {cod}(\chi ) \mid \chi \in \mathrm {Irr}(G)\}$

be the codegree set of G. Let

$\mathrm {A}_n$

be an alternating group of degree

$n \ge 5$

. We show that

$\mathrm {A}_n$

is determined up to isomorphism by

$\operatorname {cod}(\mathrm {A}_n)$

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关于交替群的编码度特征

让 G 是一个有限群，$\mathrm {Irrr}(G)$ 是 G 所有不可还原复字符的集合。定义 $\chi 在 \mathrm {Irr}(G)$ 中的codegree为 $\mathrm {cod}(\chi ):={|G：|}/{\chi (1)}$ 并且让 $\mathrm {cod}(G):=\{mathrm {cod}(\chi ) \mid \chi \in \mathrm {Irrr}(G)\}$ 是 G 的codegree集合。让 $\mathrm {A}_n$ 是一个度数为 $n\ge 5$ 的交替群。我们证明 $\mathrm {A}_n$ 是由 $\operatorname {cod}(\mathrm {A}_n)$ 同构决定的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Bulletin of the Australian Mathematical Society 数学-数学

CiteScore

1.20

自引率

14.30%

发文量

149

审稿时长

4-8 weeks

期刊介绍： Bulletin of the Australian Mathematical Society aims at quick publication of original research in all branches of mathematics. Papers are accepted only after peer review but editorial decisions on acceptance or otherwise are taken quickly, normally within a month of receipt of the paper. The Bulletin concentrates on presenting new and interesting results in a clear and attractive way. Published Bi-monthly Published for the Australian Mathematical Society